Lenny Conundrum, Round 178: What is the total area...?

[sweet_candy_500]

Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) has three fields. One field is an equilateral triangle, one field is a circle, and one field is a square. The square field is 75% larger in area than the triangular field, and 50% larger in area than the circular field. In order to completely fence all three of the fields, exactly 4000 metres of fencing is required.

What is the total area of all three fields, in square metres?

 

[stapel]

Notice: Since this is not a math-homework question, and since Neopets has been fairly clear on its position regarding people posting the prize-winning answer before the Lenny puzzle contest closes, kindly please refrain from posting solutions until after Wednesday, 16 August 2006.

If the poster cares to show some effort and progress, replying with hints and suggestions would probably be acceptable.

Thank you for your consideration.

Eliz.

 

[mcrae]

sides of the square are x, sides of the tringle are s, r is radius of the circle

x^2 = 1.75(s^2 3^(1/2))/4 = 1.5 pi r^2

4x +2s +2pi r =4000

im stuck.

 

[stapel]

Relate the areas to express "s" and "r" in terms of "x".

Eliz.

 

[TchrWill]

Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) has three fields. One field is an equilateral triangle, one field is a circle, and one field is a square. The square field is 75% larger in area than the triangular field, and 50% larger in area than the circular field. In order to completely fence all three of the fields, exactly 4000 metres of fencing is required.

What is the total area of all three fields, in square metres?

Area = A = x^2 + (1.5)3.14R^2 = 1.75(.866)s^2/2

x^2 = (1.5)3.14R^2 or R = x/2.1708

x^2 = 1.75(0.866)s^2/2 or s = x/0.87048

4x + 2(Pi)x/2.1708 + 3x/0.87048 = 4000 from which x = 387.177

I'm sure you can take it from here.